2,381 research outputs found
Counterexample Generation in Probabilistic Model Checking
Providing evidence for the refutation of a property is an essential, if not the most important, feature of model checking. This paper considers algorithms for counterexample generation for probabilistic CTL formulae in discrete-time Markov chains. Finding the strongest evidence (i.e., the most probable path) violating a (bounded) until-formula is shown to be reducible to a single-source (hop-constrained) shortest path problem. Counterexamples of smallest size that deviate most from the required probability bound can be obtained by applying (small amendments to) k-shortest (hop-constrained) paths algorithms. These results can be extended to Markov chains with rewards, to LTL model checking, and are useful for Markov decision processes. Experimental results show that typically the size of a counterexample is excessive. To obtain much more compact representations, we present a simple algorithm to generate (minimal) regular expressions that can act as counterexamples. The feasibility of our approach is illustrated by means of two communication protocols: leader election in an anonymous ring network and the Crowds protocol
Generating Diagnoses for Probabilistic Model Checking Using Causality
One of the most major advantages of Model checking over other formal methods of verification, its ability to generate an error trace in case of a specification falsified in the model. We call this trace a counterexample. However, understanding the counterexample is not that easy task, because model checker generates usually multiple counterexamples of long length, what makes the analysis of counterexample time-consuming as well as costly task. Therefore, counterexamples should be small and as indicative as possible to be understood. In probabilistic model checking (PMC) counterexample generation has a quantitative aspect. The counterexample in PMC is a set of paths in which a path formula holds, and their accumulative probability mass violates the probability bound. In this paper, we address the complementary task of counterexample generation which is the counterexample diagnosis in PMC. We propose an aided-diagnostic method for probabilistic counterexamples based on the notion of causality and responsibility. Given a counterexample for a Probabilistic CTL (PCTL) formula that doesn’t hold over Discreet-Time-Markov-Chain (DTMC) model, this method guides the user to the most responsible causes in the counterexample.</p
High-level Counterexamples for Probabilistic Automata
Providing compact and understandable counterexamples for violated system
properties is an essential task in model checking. Existing works on
counterexamples for probabilistic systems so far computed either a large set of
system runs or a subset of the system's states, both of which are of limited
use in manual debugging. Many probabilistic systems are described in a guarded
command language like the one used by the popular model checker PRISM. In this
paper we describe how a smallest possible subset of the commands can be
identified which together make the system erroneous. We additionally show how
the selected commands can be further simplified to obtain a well-understandable
counterexample
QuantUM: Quantitative Safety Analysis of UML Models
When developing a safety-critical system it is essential to obtain an
assessment of different design alternatives. In particular, an early safety
assessment of the architectural design of a system is desirable. In spite of
the plethora of available formal quantitative analysis methods it is still
difficult for software and system architects to integrate these techniques into
their every day work. This is mainly due to the lack of methods that can be
directly applied to architecture level models, for instance given as UML
diagrams. Also, it is necessary that the description methods used do not
require a profound knowledge of formal methods. Our approach bridges this gap
and improves the integration of quantitative safety analysis methods into the
development process. All inputs of the analysis are specified at the level of a
UML model. This model is then automatically translated into the analysis model,
and the results of the analysis are consequently represented on the level of
the UML model. Thus the analysis model and the formal methods used during the
analysis are hidden from the user. We illustrate the usefulness of our approach
using an industrial strength case study.Comment: In Proceedings QAPL 2011, arXiv:1107.074
PrIC3: Property Directed Reachability for MDPs
IC3 has been a leap forward in symbolic model checking. This paper proposes
PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic
model checking of MDPs. Our main focus is to develop the theory underlying
PrIC3. Alongside, we present a first implementation of PrIC3 including the key
ingredients from IC3 such as generalization, repushing, and propagation
Safety-Aware Apprenticeship Learning
Apprenticeship learning (AL) is a kind of Learning from Demonstration
techniques where the reward function of a Markov Decision Process (MDP) is
unknown to the learning agent and the agent has to derive a good policy by
observing an expert's demonstrations. In this paper, we study the problem of
how to make AL algorithms inherently safe while still meeting its learning
objective. We consider a setting where the unknown reward function is assumed
to be a linear combination of a set of state features, and the safety property
is specified in Probabilistic Computation Tree Logic (PCTL). By embedding
probabilistic model checking inside AL, we propose a novel
counterexample-guided approach that can ensure safety while retaining
performance of the learnt policy. We demonstrate the effectiveness of our
approach on several challenging AL scenarios where safety is essential.Comment: Accepted by International Conference on Computer Aided Verification
(CAV) 201
On minimising the maximum expected verification time
Cyber Physical Systems (CPSs) consist of hardware and software components. To verify that the whole (i.e., software + hardware) system meets the given specifications, exhaustive simulation-based approaches (Hardware In the Loop Simulation, HILS) can be effectively used by first generating all relevant simulation scenarios (i.e., sequences of disturbances) and then actually simulating all of them (verification phase). When considering the whole verification activity, we see that the above mentioned verification phase is repeated until no error is found. Accordingly, in order to minimise the time taken by the whole verification activity, in each verification phase we should, ideally, start by simulating scenarios witnessing errors (counterexamples). Of course, to know beforehand the set of such scenarios is not feasible. In this paper we show how to select scenarios so as to minimise the Worst Case Expected Verification Tim
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